U.S. Pat. No. 4,041,845, which is assigned to the same assignee as the present application, discloses a hydraulic elevator jack which includes a travel limit structure for the plunger which generates a hydraulic retarding force programmed by a resilient device during a travel limit stop. While this hydraulic jack performs well, it would be desirable, and it is the object of this invention, to significantly reduce the vibration and jerk rate associated with hydraulic elevator jacks, to improve not only the hydraulic elevator jack disclosed in the hereinbefore mentioned U.S. patent, but hydraulic elevator jacks in general.